A connection between aperiodic - never repeating - tiles and quantum error correction. A clearly written piece about something odd and potentially useful.
snip
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Interest turned into fascination when Boyle mentioned a special property of aperiodic tilings: local indistinguishability. In that context, the term means something different. The same set of tiles can form infinitely many tilings that look completely different overall, but it’s impossible to tell any two tilings apart by examining any local area. That’s because every finite patch of any tiling, no matter how large, will show up somewhere in every other tiling.
“If I plop you down in one tiling or the other and give you the rest of your life to explore, you’ll never be able to figure out whether I put you down in your tiling or my tiling,” Boyle said.
To Li, this seemed tantalizingly similar to the definition of local indistinguishability in quantum error correction. He mentioned the connection to Boyle, who was instantly transfixed. The underlying mathematics in the two cases was quite different, but the resemblance was too intriguing to dismiss.
Li and Boyle wondered whether they could draw a more precise connection between the two definitions of local indistinguishability by building a quantum error-correcting code based on a class of aperiodic tilings. They continued talking through the entire two-hour shuttle ride, and by the time they arrived in Toronto they were sure that such a code was possible — it was just a matter of constructing a formal proof.
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a tip of the hat to Greg
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